Khramenkov V A, Dmitrichev A S, Nekorkin V I
Department of Nonlinear Dynamics, Institute of Applied Physics of RAS, 46 Ulyanov Str., 603950 Nizhny Novgorod, Russia.
Chaos. 2022 Nov;32(11):113116. doi: 10.1063/5.0093980.
We consider several topologies of power grids and analyze how the addition of transmission lines affects their dynamics. The main example we are dealing with is a power grid that has a tree-like three-element motif at the periphery. We establish conditions where the addition of a transmission line in the motif enhances its stability or induces Braess's paradox and reduces stability of the entire grid. By using bifurcation theory and nonlocal stability analysis, we show that two scenarios for Braess's paradox are realized in the grid. The first scenario is well described and is associated with the disappearance of the synchronous mode. The second scenario has not been previously described and is associated with the reduction of nonlocal stability of the synchronous mode due to the appearance of asynchronous modes. The necessary conditions for stable operation of the grid, under the addition of a line, are derived. It is proved that the new scenario for Braess's paradox is realized in the grids with more complex topologies even when several lines are added in their bulks.
我们考虑了几种电网拓扑结构，并分析了输电线路的增加如何影响其动态特性。我们主要研究的例子是一个在周边具有树状三元 motif 的电网。我们确定了在 motif 中添加一条输电线路可增强其稳定性或引发布雷斯悖论并降低整个电网稳定性的条件。通过使用分岔理论和非局部稳定性分析，我们表明电网中实现了布雷斯悖论的两种情况。第一种情况已得到充分描述，与同步模式的消失有关。第二种情况此前未被描述，与由于异步模式的出现导致同步模式的非局部稳定性降低有关。推导了在添加线路情况下电网稳定运行的必要条件。证明了即使在具有更复杂拓扑结构的电网中大量添加多条线路时，布雷斯悖论的新情况也会出现。
